I would prefer to always rubber mount if possible but not radiators are rubber mounted. My jeep is hard mounted from the factory. Rubber mount is nice but not mandatory.
Check out the grommets used on a Lexus GX 470 radiator, any year. You would have to weld a short piece of tubing to the mounting flange of the radiator to put the grommets in and they are big, like 1.75" in dia. probably, but 4 will certainly do the job, it's what I plan on doing with mine. There are cheaper ways but they're super slick and ready to go.
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Erik
69 Camaro
Several other things with wheels and engines
I'm trying to figure out how to mount my C&R in my 69 firebird too. They must use the term "bolt in" pretty loosely I think. None of the bolt holes seem to line up with holes in the core support. I think I am going to have to cut and modify the core support to open it up so the rad sees all the air it needs. Mine came with 2 sets of the rubber nuts and bolts. Did you get yours mounted yet?